Investment in Scotland's Railways is brilliant, both on the internal services and the anglo-scottish links!
1. A plentiful fleet of largely modern DMUs (Lots of Turbostars) which means that Scotrail can run five and six carriage trains as demand requires.
2. Widespread electrification of the central belt ongoing at the moment, with brand new EMUs.
3. Line reopenings: Newcraighall, Alloa, Airdrie to Bathgate, Larkhall and the Borders Railway.
4. Fast, regular links to London with modern electric Intercity trains from both Glasgow and Edinburgh, and direct trains to London from Aberdeen and Inverness.
I don't see 125mph as a moderate speed: Britain has some of the fastest classic Intercity routes in Europe: Ideally, High Speed 2 needs to reach Scotland in order to provide much increased speeds from central England and London, as upgrades to the ECML and WCML can only go so far: I think that some upgrading of the ECML in Northumberland and the borders would go quite a way to help though: Station passing loops would be a smart move, to allow the fast trains to overtake the stoppers on what is pretty much entirely a two track railway.